> > Hi Ben, > > > > Thanks for the brain teaser! As a sometimes believer in > Occam's Razor, I > > think it makes sense to assume that Xi and Xj are indepenent, > unless we know > > otherwise. This simplifies things, and is the "rational" thing > to do (for > > some definition of rational ;->). So why not construct a bayes > net modeling > > the distributions, with causal links only where you _know_ two > variables are > > dependent? For reasoning about "orphan variables" (e.g., you > know nothing > > at all about Xi), just assume the average of all other > distributions. If > > you have P(Xi|Xj), and want P(Xj|Xi), fudge something together > with Bayes' > > rule. This isn't a complete solution, but its how I would > start... Is this > > one of the things you've tried? > > > > Cheers, > > Moshe
Well, the Novamente PTL (probabilistic term logic) module is not a Bayes net, but it has some similarities. It is based on elementary probability theory, and its two main rules are * inversion, which is just Bayes rule for guessing P(B|A) from P(A|B) (with help from P(A) and P(B) ) * deduction, which is indeed based on an independence assumption, which goes from P(A|B) and P(C|A) to P(C|B) There are variants of the deduction rule to use when dependency information is known; otherwise independency is assumed. A major difference from a Bayes net however, is that PTL doesn't impose a hierarchical structure like a Bayes net does. In a realistically complex web of probabilistic relationships, one is going to have heterarchical interdependencies, and no hierarchy will capture what's going on. Each P(A|B) corresponds to an InheritanceLink in Novamente, but, these links don't need to form a hierarchy. There is more similarity between PTL and "loopy Bayes nets", but those are kinda hacky -- they involve using algorithms proved correct for hierarchies, and just applying them to heterarchies and hoping for the best. PTL is designed to work with nonhierarchical probability webs... -- Ben ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
